Search results for "Nonexpansive mappings"

showing 3 items of 3 documents

On the structure of the set of equivalent norms on ℓ1 with the fixed point property

2012

Abstract Let A be the set of all equivalent norms on l 1 which satisfy the FPP. We prove that A contains rays. In fact, every renorming in l 1 which verifies condition (⁎) in Theorem 2.1 is the starting point of a (closed or open) ray composed by equivalent norms on l 1 with the FPP. The standard norm ‖ ⋅ ‖ 1 or P.K. Linʼs norm defined in Lin (2008) [12] are examples of such norms. Moreover, we study some topological properties of the set A with respect to some equivalent metrics defined on the set of all norms on l 1 equivalent to ‖ ⋅ ‖ 1 .

CombinatoricsDiscrete mathematicsRenorming theoryApplied MathematicsNorm (mathematics)Fixed-point theoremNonexpansive mappingsFixed point theoryEquivalence of metricsFixed-point propertyStabilityAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings

2006

Abstract It is shown that if the modulus Γ X of nearly uniform smoothness of a reflexive Banach space satisfies Γ X ′ ( 0 ) 1 , then every bounded closed convex subset of X has the fixed point property for nonexpansive mappings. In particular, uniformly nonsquare Banach spaces have this property since they are properly included in this class of spaces. This answers a long-standing question in the theory.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsUniformly nonsquare spacesApproximation propertyEberlein–Šmulian theoremBanach spaceNonexpansive mappingsUniformly convex spaceBanach manifoldFixed-point propertyNearly uniform smoothnessFixed pointsReflexive spaceLp spaceAnalysisMathematicsJournal of Functional Analysis
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MR2410211 (2009b:47107) Păcurar, Mădălina Viscosity approximation of fixed points with $\phi$-contractions. Carpathian J. Math. 24 (2008), no. 1, 88-…

2009

Let T be a nonexpansive self-mapping of a closed bounded convex subset Y of a Hilbert space. For l in (0, 1), the author considers the iteration xl = lf(xl)+(1−l)Txl, where f from Y to Y is a $\phi$-contraction. Then, the author proves that (xl)l converges strongly as l goes to 0 to the unique fixed point of the $\phi$-contraction Pof, where P is the metric projection of Y onto the set FT of fixed points of T. The viscosity approximation method of the paper is obtained from the method proposed by A. Moudafi [J. Math. Anal. Appl. 241 (2000), no. 1, 46–55; MR1738332 (2000k:47085)] for mappings in Hilbert spaces, and by H. K. Xu [J. Math. Anal. Appl. 298 (2004), no. 1, 279–291; MR2086546 (2005…

Settore MAT/05 - Analisi MatematicaNonexpansive mappings fixed point viscosity approximation $\phi$-contraction.
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